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Algebra Seminar
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Andrew Mathas
University of Sydney

Elementary divisors of Specht modules

Friday 19th March, 12:05-12:55pm, Carslaw 373.

Let H be the Iwahori-Hecke algebra of the symmetric group; this is a "deformation" of the group algebra of the symmetric group which arises naturally in the representation theory of the (finite) general linear groups. If H is semisimple, then its irreducible representations are known as the Specht modules. In the non-semisimple case each irreducible representation arises as the quotient of some Specht module by its radical.

The Specht modules of H come equipped with a natural bilinear form and one can use this form to define a Gram matrix for the Specht module (relative to some fixed basis). In this talk we will explain what is known about the elementary divisors of these Gram matrices, including giving a beautiful connection between the elementary divisors of a Specht module and its dual.

This is joint work with Matthias Kuenzer (Ulm).